Journal of Theoretical Probability

, Volume 25, Issue 2, pp 536–564

Asymptotic Theory for Fractional Regression Models via Malliavin Calculus


DOI: 10.1007/s10959-010-0302-y

Cite this article as:
Bourguin, S. & Tudor, C.A. J Theor Probab (2012) 25: 536. doi:10.1007/s10959-010-0302-y


We study the asymptotic behavior as n→∞ of the sequence
where \(B^{H_{1}}\) and \(B^{H_{2}}\) are two independent fractional Brownian motions, K is a kernel function and the bandwidth parameter α satisfies certain hypotheses in terms of H1 and H2. Its limiting distribution is a mixed normal law involving the local time of the fractional Brownian motion \(B^{H_{1}}\). We use the techniques of the Malliavin calculus with respect to the fractional Brownian motion.


Limit theoremsFractional Brownian motionMultiple stochastic integralsMalliavin calculusRegression modelWeak convergence

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.SAMMUniversité de Paris 1 Panthéon-SorbonneParisFrance
  2. 2.Laboratoire Paul PainlevéUniversité de Lille 1Villeneuve d’AscqFrance